With the advent of modern technologies, including the IoT and blockchain, smart-parking (SP) systems are becoming smarter and smarter. Similar to other automated systems, and particularly those that require automation or minimal interaction with humans, the SP system is heuristic in delivering performances, such as throughput in terms of latency, efficiency, privacy, and security, and it is considered a long-term cost-effective solution. This study looks ahead to future trends and developments in SP systems and presents an inclusive, long-term, effective, and well-performing smart autonomous vehicle parking (SAVP) system that explores and employs the emerging fog-computing and blockchain technologies as robust solutions to strengthen the existing collaborative IoT–cloud platform to build and manage SP systems for autonomous vehicles (AVs). In other words, the proposed SAVP system offers a smart-parking solution, both indoors and outdoors, and mainly for AVs looking for vacant parking, wherein the fog nodes act as a middleware layer that provides various parking operations closer to IoT-enabled edge devices. To address the challenges of privacy and security, a lightweight integrated blockchain and cryptography (LIBC) module is deployed, which is functional at each fog node, to authorize and grant access to the AVs in every phase of parking (e.g., from the parking entrance to the parking slot to the parking exit). A proof-of-concept implementation was conducted, wherein the overall computed results, such as the average response time, efficiency, privacy, and security, were examined as highly efficient to enable a proven SAVP system. This study also examined an innovative pace, with careful considerations to combatting the existing SP-system challenges and, therefore, to building and managing future scalable SP systems.